A Subexponential Algorithm for Discrete Logarithms over All Finite Fields

@inproceedings{Adleman1993ASA,
  title={A Subexponential Algorithm for Discrete Logarithms over All Finite Fields},
  author={Leonard M. Adleman and Jonathan DeMarrais},
  booktitle={CRYPTO},
  year={1993}
}
There are numerous subexponential algorithms for computing discrete logarithms over certain classes of finite fields. However, there appears to be no published subexponential algorithm for computing discrete logarithms over all finite fields. We present such an algorithm and a heuristic argument that there exists a c ? R > 0 such that for all sufficiently large prime powers pn, the algorithm computes discrete logarithms over GF(pn) within expected time: ec(log(pn)log log(pn))1/2. 

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References

Publications referenced by this paper.
SHOWING 1-10 OF 23 REFERENCES

Discrete Logarithms in Finite Fields and Their Cryptographic Significance

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Fast evaluation of logarithms in fields of characteristic two

  • Don Coppersmith
  • Mathematics, Computer Science
  • IEEE Trans. Information Theory
  • 1984
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

Fast Computation of Discrete Logarithms in GF(q)

VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

Fermat’s Last Theorem

VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Discrete Logarithms in GF(P) Using the Number Field Sieve